How do I get the name of the active brush texture with Python?
In this case, you can reference it from the brush it is applied to:

bpy.data.brushes['NameOfBrush'].texture


Or use the active brush (if the context is sculpt mode, texture mode, etc.):

bpy.context.brush.texture


Or:

bpy.context.sculpt.brush.texture


https://www.blender.org/api/blender_python_api_current/info_api_reference.html#indirect-data-access